Please help! I am giving brainiest if you answer correctly.

Belinda is thinking about buying a house for $179,000. The table below shows the projected value of two different houses for three years:

Number of years 1 2 3

House 1 (value in dollars) 186,160 193,606.40 201,350.66

House 2 (value in dollars) 190,000 201,000 212,000

Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points)

Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points)

Part C: Belinda wants to purchase a house that would have the greatest value in 30 years. Will there be any significant difference in the value of either house after 30 years? Explain your answer, and show the value of each house after 30 years. (4 points)

  A. House 1, exponential; House 2, linear

  B. House 1, f(x) = 179000·1.04^x; House 2, f(x) = 179000 +11000x

  C. House 1, $580,600; House 2, $509,000; about a 14% difference

Step-by-step explanation:

A. Your first clue that the values of House 1 are from an exponential function is that they have decimal points. Also, they do not have a common difference, so cannot be from a linear function.

The differences in value from year-to-year for House 2 are constant at $11,000. That value function is linear.

Given the two choices, ...

  House 1 value is represented by an exponential function

  House 2 value is represented by a linear function

__

B. The year-on-year ratio of values for House 1 is ...

  186,160/179,000 ≈ 1.04

So, the exponential function can be written as ...

  f(x) = (initial value)·(growth factor)^x

  f(x) = 179,000·1.04^x . . . . value function for House 1

The value function for House 2 has already been seen to increase from its initial value of 179,000 by 11,000 per year. That value function is ...

  f(x) = 179,000 +11,000x . . . . value function for House 2

__

C. The value of House 1 after 30 years is ...

  f(30) = 179,000·1.04^30 ≈ 580,568

The value of House 2 after 30 years is ...

  f(30) = 179,000 +11,000·30 = 509,000

The difference in value is $71,568, about 14% of the value of House 2. Belinda might consider this difference to be significant.

_____

Comment on "significant"

In estimating terms, a difference of less than 10% is usually not considered significant. In some markets, margins are so thin that a difference in value of 14% would be considered to be extremely significant. The significance is in the eye of the beholder. No guidance is given here, so it is difficult to say whether the difference in value is significant or not.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

so, converting firstly the mixed fractions to improper fractions and then "adding".